SOCW 671 #11 Correlation and Regression

Uses of Correlation To study the strength of a relationship To study the direction of a relationship Scattergrams are used to display data

Types of Correlation Perfect Correlations: -1.0 or 1.0 Nonperfect Correlations: everything else Strength and Direction: - or +; near 0.0 weak; near –1.0 or 1.0 strong Represented by “r.” Interpreting Linear Correlations Correlation Continuum: -1.0 to 1.0

Coefficient of Determination Proportion of the variation in one variable that accounts for (or related to) the variation in the other variable R-squared).

Using Correlation for Description  Can be used as a mathematical alternative to the scatterplot.  Pearson Product-Moment Coefficient: a parametric measure of the strength of a correlation. Need two interval or ratio level variables.  Spearman’s rho: a nonparametric measure that uses ordinal level variables

Bivariate & Multiple Correlation Bivariate (two variables) vs. Multiple Correlation (three or more variables)  Partial R: removes the influence of a third (intervening) variable Multiple R: uses one criterion (dependent) variable and two or more predictor (independent) variables.

Regression Can be used to  predict  explain  describe

Regression Line Computation of the regression line: Y’ = a + b(X)  Regression Coefficient (b): slope of the line  The y-Intercept (a): the starting point of the line  Predicted Y (Y’): estimated score for the criterion value

Least-squares Criterion The process of fitting a line to the data Minimizes the differences of expected to actual values

Selecting Correct Statistical Test Five considerations  Sampling methods  Distribution of the dependent (and sometimes the independent variable) within the population  Level of measurement of the independent and dependent variables  Statistical power of the test  Robustness of the test